ERT250 DYNAMICS
PRE-REQUISITE: ENGINEERING MECHANICS/STATIC
Course Synopsis
The course covers
• the kinematics of particles which includes
displacement, velocity and acceleration,
• kinetics of particles; Newton’s law of motion,
equation of motion, work, impulse, momentum,
principle of work and energy, principle of impulse
and momentum,
• planar kinetics and kinematics of rigid bodies,
three dimensional kinematics of rigid bodies, three
dimensional kinetics of rigid bodies and
• mechanical vibration.
Course Outcomes
• CO1: Ability to analyze the problems in the kinematics
of particle and rigid body.
• CO2: Ability to analyze problems related to kinetics of
particle involving force and acceleration, work, energy
and momentum.
• CO3: Ability to evaluate the problems in the kinetics of
rigid bodies in 2D and 3D.
• CO4: Ability to formulate the solutions of the problems
for damped and undamped vibrations.
Course Evaluation
• Continuous Assessment
– Assignments
20 %
– Quizzes
10 %
• Examination
– Mid term Examinations
20 %
– Final Examination
50 %
LECTURES AND TUTORIAL
• 2 hours lectures/week
• 1 hour tutorial/week
TEXT BOOK & REFERENCES BOOKS
INTRODUCTION TO DYNAMICS
• HISTORY AND MODERN APPLICATIONS
• BASIC CONCEPTS
• NEWTON’S LAWS
• UNITS
• DIMENSIONS
• GRAVITATION
• SOLVING PROBLEMS IN DYNAMICS
• QUIZ 1
An Overview of Mechanics
Mechanics
The study of how bodies react to forces
acting on them.
Statics
The study of bodies in
equilibrium.
Dynamics
1. Kinematics –
concerned with
the geometric
aspects of motion
2. Kinetics concerned with
the forces causing
the motion
HISTORY AND MODERN APPLICATIONS
• Dynamics : branch of mechanics which deal with
motion of bodies under the action of forces.
• The study of dynamics usually follow the study of
statics; which deals with the effect of _________ on
bodies in __________.
• Dynamics has two parts:
– _____________: the study of motion without the reference to
the forces to cause motion
– _____________: relates the action of forces on bodies to
their resulting motions
History of Dynamics
• The beginning of rational understanding
of dynamics is credited to Galileo Galilei
(1564-1642), who made observations
concerning:
– bodies in free fall,
– motion on incline plane and
– motion of pendulum
• Newton (1642-1727), guided by Galileo’s
work, was able to make an accurate
formulation of the laws of motion. Newton
was first to correctly formulate the law of
universal gravitation.
Applications of Dynamics
• The principles of mechanics dynamics:
– Basic to analysis and design of moving structures
– To fixed structures subject to shock loads
– To robotic and automatic control systems
– To rocket, missile and spacecraft
– To ground and space transportation
– To machinery of all types : turbines, pumps, reciprocating
machines, hoists, and machine tool
• In Biosystems and Agricultural Engineering?
BASIC CONCEPTS
• Space
• Time
• Mass
• Force
• Particle
• Rigid body
• Vector and scalar
NEWTON’S LAWS
F = ma
• Law I :
– A particle remains at rest or continuous to move with
uniform velocity if there is no force acting on it.
• Law II
– The acceleration of a particle is proportional to the resultant
force acting on it and is in the direction of this force.
• Law III
– The forces of action and reaction between interacting
bodies are equal in magnitude, opposite in direction and
collinear.
UNITS
• SI Units
Quantity
Dimensional
Symbol
SI Unit
Unit
Symbol
Mass
M
kg
kg
Length
L
meter
m
Time
T
second
s
Force
F
newton
N
1 N = 1 kg/m.s2
DIMENSIONS
• The principle of dimensional homogeneity: all physical
relations must be dimensionally homogeneous.
• Example:
• F = ML/T2
• Fx = ½ mv2
GRAVITATION
• Newton’s Law of gravitation
m1m2
Fg 
r2
G  constant of proportion ality
G  Universal Gravitatio nal Constant
G  6.67 x10  27 Nm
Fg  G
2
kg 2
m1m2
r2
Fg  mg  Use this when you are on the earth
Fg  G
m1m2
 Use this when you are LEAVING th e earth
r2
Effect of Altitude
Mm
mg  G 2
r
(6.67 x1027 )(5.97 x1024 )
2
M
g


9
.
81
m
/
s
g G 2
6 2
(
6
.
37
x
10
)
r
M  Mass of the Earth  5.97 x10 24 kg
r  radius of the Earth  6.37 x10 6 m
The variation of g with altitude is easily determined from the
gravitational law.
If go represents the absolute acceleration due to gravity at sea
level, the absolute value at altitude h is
r2
g  go
r  h 2
r  radius of the Earth  6.37 x10 6 m
Apparent Weight
• The gravitational attraction of the earth on a body.
• If a force of attraction of true weight of the body, W,
because the body falls with absolute acceleration, g
gives
• W = mg
SOLVING PROBLEMS IN DYNAMICS
-Steps
1. Formulate the problem
–
State the given data
–
State the desired result
–
State your assumption and approximation
2. Develop the solution
–
Draw any needed diagram and include coordinate
appropriate for the problem
–
State the principles to be applied to your solution; formula
–
Make your calculation
–
Used consistent unit
–
Ensure the answer are reasonable in term of magnitude and
directions, etc
–
Draw conclusion
Key note
• Don’t simply memorize the kinetics and kinematics
equations but expose to the wide variety problem
situation. DO AN EXERCISES
QUIZ 1
1. State Newton’s law of motion
2. Express the law of gravitation.
3. Discuss the effect of altitude and rotation of the
earth on the acceleration due to gravity.
4. A space-shuttle module has a mass of 50 kg and
rests on the surface of the earth at latitude of 45o
north.
a. Determine the surface level weight of the module.
b. The module is taken to an altitude of 300 km
above the surface of the earth, determine its
weight under this condition.
c. If a cargo bay is fixed inside the space shuttle and
the shuttle is in a circular orbit at altitude 300 km
above the surface, determine the weight of the
module.
Thank You